For this purpose we shall suppose that the matter of which the earth is composed weighs 300 pounds per cubic foot, this being about the ascertained average. If the diameter of the earth be 7,930 miles, the whole globe will be found to contain 261,107,411,765 cubic miles, which make 1,423,499,120,882,544,640,000 cubic yards, or 38,434,476,263,828,705,280,000 cubic feet, and allowing 300 pounds to each cubic foot, we shall have 11,530,342,879,148,611,584,000,000 for the weight of the earth in pounds.
Now, we know, by the laws of mechanics, that, whatever be the construction of a machine, the space passed over by the weight, is to that passed over by the moving power, in the reciprocal ratio of the latter to the former. It is known also, that a man can act with an effort equal only to about 30 pounds for eight or ten hours, without intermission, and with a velocity of about 10,000 feet per hour. If then we suppose the machine of Archimedes to be put in motion by means of a crank, and that the force continually applied to it is equal to 30 pounds, then with the velocity of 10,000 feet per hour, to raise the earth one inch the moving power must pass over the space of 384,344,762,638,287,052,800,000 inches; and if this space be divided by 10,000 feet or 120,000 inches, we shall have for a quotient 3,202,873,021,985,725,440, which will be the number of hours required for this motion. But as a year contains 8,766 hours, a century will contain 876,600; and if we divide the above number of hours by the latter, the quotient, 3,653,745,176,803, will be the number of centuries during which it would be necessary to make the crank of the machine continually turn in order to move the earth only one inch. We have omitted the fraction of a century as being of little consequence in a calculation of this kind. The machine is also supposed to be constantly in action, but if it should be worked only eight hours each day, the time required would be three times as long.
So that while it is true that Archimedes could move the world, the space through which he could have moved it, during his whole life, from infancy to old age, is so small that even if multiplied two hundred million times it could not be measured by even the most delicate of our modern measuring instruments.